Occurrence of negative open variances in ternary systems |
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| Authors: | John C Butler |
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| Institution: | 1. Department of Geology, University of Houston, USA
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| Abstract: | Parameters of the hypothetical open arrays were computed for a total of 20 published sets of chemical analyses of igneous rocks in oxide, mole, cation, and cation weight-percentage forms. Negative open variances in the full (11 variables) data sets were eliminated by using a linear transformation of the raw data. For the 13 variables (11 oxides, the sum of the alkalies and total iron as FeO) 286 different simple ternary combinations can be formed. The CaO-Na2O-K2O (CNK) and total iron-serum of the alkalies-MgO (FMA) combinations are of frequent use in depicting “differentiation trends” within a series of igneous rocks. In each of the 20 data sets the estimated open variances of Na2O in the CNK and total iron in the FMA combinations are negative. Elimination of negative open variances in the full data array does not eliminate negative open variances in these ternary combinations. Greater than 50 percent of the 29,172 ternary combinations examined contain a negative open variance. |
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